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Algebraic Identities

If A = 3x2 – ...

Question

If $A = 3 x^{2} - 4 x + 1, B = 5 x^{2} + 3 x - 8$ and, $C = 4 x^{2} - 7 x + 3$ , then find:
(i) (A + B) – C
(ii) B + C – A
(iii) A + B + C

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Solution

(i) (A + B)– C
$= ((3 x^{2} - 4 x + 1) + (5 x^{2} + 3 x - 8)) - (4 x^{2} - 7 x + 3)$
$= (3 x^{2} - 4 x + 1 + 5 x^{2} + 3 x - 8) - 4 x^{2} + 7 x - 3$
$= 8 x^{2} - x - 7 - 4 x^{2} + 7 x - 3$
$= 4 x^{2} + 6 x - 10$

(ii) B + C – A
$= (5 x^{2} + 3 x - 8) + (4 x^{2} - 7 x + 3) - (3 x^{2} - 4 x + 1)$
$= 5 x^{2} + 3 x - 8 + 4 x^{2} - 7 x + 3 - 3 x^{2} + 4 x - 1$
$= 5 x^{2} + 4 x^{2} - 3 x^{2} + 3 x - 7 x + 4 x - 8 + 3 - 1$
$= 6 x^{2} + 0 x - 6$
$= 6 x^{2} - 6$

(iii) A + B + C
$= 3 x^{2} - 4 x + 1 + 5 x^{2} + 3 x - 8 + 4 x^{2} - 7 x + 3$
$= 12 x^{2} - 8 x - 4$

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Similar questions

A = 3 x^{2} - 4 x + 1, B = 5 x^{2} + 3 x - 8

C = 4 x^{2} - 7 x + 3

, then find:
(i)

(A + B) - C

B + C - A

A + B + C

A = 5 x^{2} + 3 x^{2} - 4 x + 1, B = 3 x^{3} + 5 x^{2} + 3 x - 8

C = 6 x^{3} - 4 x^{2} - 7 x + 3

(A + B) = C

Question 68 (i)

If $A = 3 x^{2} - 4 x + 1, B = 5 x^{2} + 3 x - 8 a n d C = 4 x^{2} - 7 x + 3$ , then find

(A + B) - C

A = 2 y^{2} + 3 x - x^{2}, B = 3 x^{2} - y^{2}

C = 5 x^{2} - 3 x y

A + B + C

Q. Roots of the equation

\frac{2 x}{{3 x}^{2} - x + 2} - \frac{7 x}{{3 x}^{2} + 5 x + 2} = 1

\frac{- a - \sqrt{b}}{c}

\frac{- a - \sqrt{b}}{c}

b - a - c

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